de Rham decomposition for Riemannian manifolds with boundary

TL;DR

This paper extends the classical de Rham decomposition theorem to Riemannian manifolds with boundary, utilizing the development of curves technique to handle the boundary case.

Contribution

It introduces a novel extension of the de Rham decomposition theorem specifically for manifolds with boundary.

Findings

Decomposition theorem successfully extended to manifolds with boundary

Development of curves is effective in boundary cases

New techniques enable analysis of manifold structures with boundary

Abstract

In this paper, we extend the classical de Rham decomposition theorem to the case of Riemannian manifolds with boundary by using the trick of development of curves.